Chapter 9: Q16. (page 566)

Describe how the graph of the given function is related to the graph of
$f (x) = x^{2} h (x) = 2 x^{2}$

Short Answer

Expert verified

The graph of $h (x) = 2 x^{2}$ is the graph of $f (x) = x^{2}$ ,vertically stretched by a factor 2.

Step by step solution

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $y = a x^{2} + b x + c$ , where, $a \neq 0$ is called the standard form of the quadratic function.

Step 2. Define the transformations of the graph of the function.

The graph of $k f (x)$ , will vertically stretch the graph of $f (x)$ by a factor $k$ if $k > 1$ and will vertically compress the graph of $f (x)$ by a factor $k$ if $0 < k < 1$ .

Step 3. Describe how the graph of hx=2x2 is related to the graph of fx=x2.

Observe the equation $h (x) = 2 x^{2}$ .

The graph is multiplied by $k = 2$ , so the graph is vertically stretched by a factor 2.

Therefore, the graph of $h (x) = 2 x^{2}$ is the graph of $f (x) = x^{2}$ , vertically stretched by a factor 2.

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Describe how the graph of the given function is related to the graph of
$f (x) = x^{2} h (x) = 2 x^{2}$

Short Answer

Step by step solution

Step 1. Define the standard form of the quadratic function.

Step 2. Define the transformations of the graph of the function.

Step 3. Describe how the graph of hx=2x2 is related to the graph of fx=x2.

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Describe how the graph of the given function is related to the graph of fx=x2hx=2x2

Short Answer

Step by step solution

Step 1. Define the standard form of the quadratic function.

Step 2. Define the transformations of the graph of the function.

Step 3. Describe how the graph of hx=2x2 is related to the graph of fx=x2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Probability and Statistics

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

Describe how the graph of the given function is related to the graph of
$f (x) = x^{2} h (x) = 2 x^{2}$